A Boring Dystopia

In addition to what everyone else has posted, FMLA also has the wonderful caveat of not coming into force until you've been at a job for one year. Yay...

For people outside of the US, FMLA is up to three months of unpaid leave where you get the privilege of getting to keep your job and your benefits (though you continue to pay for them while not being paid) if you have a medical justification to be out of work.

For many American women, this is all they have access to for maternity leave. So they power through those three months (caring for a newborn no less) then have to scrap together the cash to put their 4 month old in day care ($15 to $20k annually) while not getting paid for that quarter of the year.

40% of infants are still breast feeding at 12 months. This means a new mom is often trying to find time at work to pump and is providing pumped milk to the daycare to be given to their child while they're working. Health officials consider only 40% to be less than ideal since breastfeeding has immunological and cognitive benefits for infants and remarkably cognitive benefits even for moms later in life. Many American women stop breast feeding at 6 months (the minimum recommended duration) since pumping at work becomes too cumbersome. 

Around 40 to 45% of women in the US don't even qualify for FMLA because your employer needs to be large enough (50+ employees) and you need to have worked for them long enough (usually a year) to qualify.

Blue states fill the gap with their own state run programs (still usually only three months, though you get some pay) but if you're in a red state the choice for many women is 1) have children and enter financial ruin or 2) don't have children.

America lags behind most advanced economies in this regard and there isn't any sign of these circumstances improving.

the right to take the time off, not the right to be paid for it.

FMLA? Some kind of US maternity leave?

That's the employer's responsibility, not yours